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POINTWISE CONVERGENCE OF AVERAGES ALONG CUBES Abstract. Let (X, B, , T) be a measure preserving system. We prove the pointwise
 

Summary: POINTWISE CONVERGENCE OF AVERAGES ALONG CUBES
I. ASSANI
Abstract. Let (X, B, , T) be a measure preserving system. We prove the pointwise
convergence of the averages
1
N2
N-1
n,m=0
f1(Tn
x)f2(Tm
x)f3(Tn+m
x)
and of similar averages with seven bounded functions.
1. Introduction
In [3], V. Bergelson generalized Khintchine's theorem [6] by proving the L2 convergence
of the averages
1
N2
N-1
n,m=0

  

Source: Assani, Idris - Department of Mathematics, University of North Carolina at Chapel Hill

 

Collections: Mathematics